I started my writing career with Stage Plays. I'll put this in the context of being based in London, the UK, where there has always been a very strong Fringe / Independent Theatre scene, which has only increased in recent years with a number of new smaller independent, off-west end (The same as Off-Broadway kind of) venues which support emerging playwrights as well as more traditional work.
Between 1997 and about 2005 I did 8 Theatre productions, all of which I wrote but also directed and was involved in the production side as well. I ran my own Theatre Company during that time. Where basically the money from one production would fund the next and so on. I was lucky in the sense that when I moved back to the city in 1997 there was a Theatre just up the road from where I lived which was looking for new work, so I did my first production there before the end of 1997 which as luck would have it sold out, which got my foot in the door so to speak. I used theatre as a way of developing my writing skills, but also as a way of reaching out to actors I wanted to work with. There was also a very good Acting Improvisation Class which had been started by the actor Dexter Fletcher and later his brother Graham (American readers would know him from Band of Brothers, British from shows like Press Gang, more recently he is a director, his last film was Eddie The Eagle) His class was rich with talent and they were in the same building, so that was very handy.
In UK terms we don't have the same issues as you with the Unions, so anything that is performed can get published. It just depends on the success of the play itself and if you can manage to get you play transferred from the off West End venue, to the West End, or get a big producer to come and see it. That was always the most important thing back then, either to get a transfer or to get more work out of it. Back then the internet was only just beginning and you didn't have forums or social media when I started out in Theatre so you had to literally give out flyers on the streets and work really hard to get people to come to your shows (To some degree you still have to do that now, but can do much more online)
Putting on a play in the UK will mean the British Libary will automatically contact you and ask for a hard copy of your production so it is stored in their archives and there will always be a copy of it for time and memorium. I have to confess I did not always get copies of my plays to them, I know that will sound incredible and people must be screaming at me, saying why the hell not? The problem is when you're producing and directing something, and basically working for free essentially, you barely have time to do anything else and you never have enough time (or money) to do all the things you need to do as it is, so running down to Kings Cross and getting the copy sorted out for them was never at the forefront of my mind in the middle of a production and I would normally go straight from one to the other.
I came back to stage productions again when I was asked to co-write a play by a friend of mine in 2008 about her life and the abuse she had suffered at the hands of her Father when she was younger. We were halfway through completing it when she died of a brain aneurysm in 2009. I completed the play on my own and put it on in 2010 and it was a disaster which was a learning curve and I considered myself a veteran. It also showed me at the time how things had changed with social media and what would sell and what wouldn't, depending on how you were able to treat a subject and promote it within the means you had available. (Unknown cast won't sell a play about a heavy subject unless you have very clever marketing, but name stars can)
I also wrote another stage play last year, my first in some time, The Seven Young Guns of Hollywood, based on the making of the original Magnificent Seven film with Steve McQueen and Yul Brynner, about all the goings on behind the making of the film, which we did a read through of in July of 2017. I've given this overview of my theatre experience in this thread, so that if I can ever offer anyone any advice in this world, then please do feel free to give me a shout, its something I certainly have had my fair share of experiences in, both good and bad and if I cannot help you, I certainly will know someone who can.
PUBLISHING - Yeah, this is a hard one. If you were someone with a good cult following already, or say 50,000 loyal readers, even if they're from all over the world and you wanted to publish a play. I would say do it, because if you have that momentum or fanbase behind you anyway, I am sure a good percentage of them would love to read it and your basically publishing a script/play for profit and this can also be a good way to get it read by lots of people, some of whom might even want to pay you royalties/fees to stage it - but if you don't have that behind you, then its going to be as tough a sell as a novel. I think there is a market out there for this stuff, but people are only going to read it if they're already familiar with your work. You also have to remember unlike film and television and an actual novel, which is around for ever, Theatre is a visceral but temporary experience, normally brought to life just the once (Unless your a die hard fan who repeatedly watches the same show) for the audience member and then is often forgotten, so it doesn't have the same fan base as say cult books or shows, which can easily be obtained or watched or read, or passed down. From time to time I still meet people who saw a play we put back on in 1998 or 2001, but believe that happens once every few years if I am lucky. So consider those terms as well. If you haven't written a play before though, I urge you to do it, or work with a local Theatre / Drama group and devise one because there is nothing quite like seeing your own work brought to life on stage right before your very eyes. When done well, that is an unbeatable memory which as a writer will stay with you for a very long time.